Resources tagged with Mathematical reasoning & proof similar to Plutarch's Boxes:
Other tags that relate to Plutarch's Boxes
Cuboids. Fractions. Volume and capacity. Mathematical reasoning & proof. Algebra - generally. Inequality/inequalities. Calculating with fractions. Diophantine equations. Other equations. Surface and surface area.There are 172 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical reasoning & proof
Our Ages
Age 14 to 16 Challenge Level:
I am exactly n times my daughter's age. In m years I shall be ... How old am I?
Diophantine N-tuples
Age 14 to 16 Challenge Level:
Can you explain why a sequence of operations always gives you perfect squares?
DOTS Division
Age 14 to 16 Challenge Level:
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
For What?
Age 14 to 16 Challenge Level:
Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.
Unit Fractions
Age 11 to 14 Challenge Level:
Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.
Euler's Squares
Age 14 to 16 Challenge Level:
Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...
Converse
Age 14 to 16 Challenge Level:
Clearly if a, b and c are the lengths of the sides of an equilateral triangle then a^2 + b^2 + c^2 = ab + bc + ca. Is the converse true?
Mouhefanggai
Age 14 to 16
Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.
There's a Limit
Age 14 to 18 Challenge Level:
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?
Square Mean
Age 14 to 16 Challenge Level:
Is the mean of the squares of two numbers greater than, or less than, the square of their means?
Archimedes and Numerical Roots
Age 14 to 16 Challenge Level:
The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
Whole Number Dynamics V
Age 14 to 18
The final of five articles which containe the proof of why the sequence introduced in article IV either reaches the fixed point 0 or the sequence enters a repeating cycle of four values.
Whole Number Dynamics IV
Age 14 to 18
Start with any whole number N, write N as a multiple of 10 plus a remainder R and produce a new whole number N'. Repeat. What happens?
Whole Number Dynamics III
Age 14 to 18
In this third of five articles we prove that whatever whole number we start with for the Happy Number sequence we will always end up with some set of numbers being repeated over and over again.
Yih or Luk Tsut K'i or Three Men's Morris
Age 11 to 18 Challenge Level:
Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .
Whole Number Dynamics II
Age 14 to 18
This article extends the discussions in "Whole number dynamics I". Continuing the proof that, for all starting points, the Happy Number sequence goes into a loop or homes in on a fixed point.
A Knight's Journey
Age 14 to 18
This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.
Whole Number Dynamics I
Age 14 to 18
The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.
Proofs with Pictures
Age 14 to 18
Some diagrammatic 'proofs' of algebraic identities and inequalities.
Impossible Sandwiches
Age 11 to 18
In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot.
The Frieze Tree
Age 11 to 16
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
Picturing Pythagorean Triples
Age 14 to 18
This article discusses how every Pythagorean triple (a, b, c) can be illustrated by a square and an L shape within another square. You are invited to find some triples for yourself.
Postage
Age 14 to 16 Challenge Level:
The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage. . . .
Top-heavy Pyramids
Age 11 to 14 Challenge Level:
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
Fitting In
Age 14 to 16 Challenge Level:
The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest. . . .
Long Short
Age 14 to 16 Challenge Level:
What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?
Mod 3
Age 14 to 16 Challenge Level:
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
Cosines Rule
Age 14 to 16 Challenge Level:
Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.
N000ughty Thoughts
Age 14 to 16 Challenge Level:
How many noughts are at the end of these giant numbers?
A Biggy
Age 14 to 16 Challenge Level:
Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
Sixational
Age 14 to 18 Challenge Level:
The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .
Why 24?
Age 14 to 16 Challenge Level:
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
Pythagorean Triples I
Age 11 to 16
The first of two articles on Pythagorean Triples which asks how many right angled triangles can you find with the lengths of each side exactly a whole number measurement. Try it!
Angle Trisection
Age 14 to 16 Challenge Level:
It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.
Mediant Madness
Age 14 to 16 Challenge Level:
Kyle and his teacher disagree about his test score - who is right?
Always Perfect
Age 14 to 16 Challenge Level:
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
Logic, Truth Tables and Switching Circuits Challenge
Age 11 to 18
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
Pythagorean Triples II
Age 11 to 16
This is the second article on right-angled triangles whose edge lengths are whole numbers.
Similarly So
Age 14 to 16 Challenge Level:
ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.
Pythagoras Proofs
Age 14 to 16 Challenge Level:
Can you make sense of these three proofs of Pythagoras' Theorem?
Breaking the Equation ' Empirical Argument = Proof '
Age 7 to 18
This article stems from research on the teaching of proof and offers guidance on how to move learners from focussing on experimental arguments to mathematical arguments and deductive reasoning.
Cyclic Quadrilaterals
Age 11 to 16 Challenge Level:
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Folding Fractions
Age 14 to 16 Challenge Level:
What fractions can you divide the diagonal of a square into by simple folding?
Iffy Logic
Age 14 to 18 Challenge Level:
Can you rearrange the cards to make a series of correct mathematical statements?
Symmetric Tangles
Age 14 to 16
The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!
The Great Weights Puzzle
Age 14 to 16 Challenge Level:
You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
Geometric Parabola
Age 14 to 16 Challenge Level:
Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
L-triominoes
Age 14 to 16 Challenge Level:
L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?
NRICH is part of the family of activities in the Millennium Mathematics Project.